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What is 10x-4x?

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Updated: 4/28/2022

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How do you prove that the line y equals 2x plus 1.25 is a tangent to the curve y squared equals 10x?

If: y = 2x+5/4 and y^2 = 10x Then: y^2 = (2x+5/4)^2 So: 4x^2 +5x +25/16 = 10x Transposing terms: 4x^2 -5x +25/16 = 0 A line is tangent to a curve when the discriminant: b^2 -4ac = 0 Thus: 5^2 -4*4*25/16 = 0 Therefore: y = 2x+1.25 is a tangent to the curve y^2 = 10x

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